The Essence of Quintessence and the Cost of Compression

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Abstract
Standard two-parameter compressions of the infinite dimensional dark energy model space show crippling limitations even with current SN-Ia data. Firstly they cannot cope with rapid evolution - the best-fit to the latest SN-Ia data shows late and very rapid evolution to w_0 = -2.85. However all of the standard parametrisations (incorrectly) claim that this best-fit is ruled out at more than 2-sigma, primarily because they track it well only at very low redshifts, z < 0.2. Further they incorrectly rule out the observationally acceptable region w << -1 for z > 1. Secondly the parametrisations give wildly different estimates for the redshift of acceleration, which vary from z_{acc}=0.14 to z_{acc}=0.59. Although these failings are largely cured by including higher-order terms (3 or 4 parameters) this results in new degeneracies which open up large regions of previously ruled-out parameter space. Finally we test the parametrisations against a suite of theoretical quintessence models. The widely used linear expansion in z is generally the worst, with errors of up to 10% at z=1 and 20% at z > 2. All of this casts serious doubt on the usefulness of the standard two-parameter compressions in the coming era of high-precision dark energy cosmology and emphasises the need for decorrelated compressions with at least three parameters.Comment: 7 pages, 4 colour figures, EmulateApJ; v2: includes Bayesian evidence analysis and table that were only present in published version, because of increased interest in Bayesian model comparison (no new material beyond the one in the published ApJL of 2004